
%% Saturn
warning off
clc;clear;
format longg
options_negx = odeset('RelTol',1e-13,'AbsTol',1e-13,'Events',@NegXcrossing);
options=odeset('RelTol',1e-13,'AbsTol',1e-13);
options_fmincon = optimoptions('fmincon', 'MaxFunctionEvaluations', 5000, ...
    'MaxIterations', 5000,'ConstraintTolerance',1e-6,'Algorithm','Interior-point','stepTolerance',1e-21);
%% Inputs.
G           = 6.674e-11 * ((1/1000)^3); % Gravitational parameters

mass_central = 1.989e30;
%[] Mass of central planet

mass_moon = 5.972e24;         %Callisto
%[] mass of moons

DU = 151.73e6;           %Callisto
%[km] Semi-major axis of Moons, used as distance units for each CRTBP
%environment.

moonName = {'Luna'};
%[] Name of the Moons

thetao = 0;
%[] Initial position of the moon relative to the first point of aries

GM_central = mass_central*G;
%[] Gravitational parameters

GM_moon = mass_moon*G;
%[] Gravitational parameters

N = length(mass_moon);
%[] Number of Moons

u = zeros(N,1);
for ii = 1:N
    u(ii) = GM_moon(ii)/(GM_moon(ii)+GM_central);
end
%[] Gravataional ratio

TU = zeros(N,1);
VU = zeros(N,1);
for ii = 1:N
    TU(ii) = sqrt(DU(ii)^3/GM_central);
    VU(ii) = DU(ii)/TU(ii);
end
%[] Time constant for each crtbp system

theta_dot = zeros(1,N);
for ii = 1:length(theta_dot)
    theta_dot(ii) = sqrt(GM_central*DU(ii))/DU(ii)^2;
end
%[] Theta dot for each planet.




%% environment settings 
dt = 0.01;
startphase=0; % changing the starting position of the periodic
% orbit to show changes in the pole visibility based on the Satellite's position wrt the Sun's pole
% OpenCRTBP_u(u)
%% Define inertial frame FNs
[xs,ys,zs] = ellipsoid(-0,0,0,696340,696340,696340,500);
figure;
s = surface(xs,ys,zs);
rotate(s, [1 0 0], 7.25);
rotate(s, [0 0 1], 73.67+0.014*(2023-1850));
InclinationRotationAngle = 7.25;
RAANRotationAngle = 73.67+0.014*(2023-1850);
PoleDirection = Rotation([0;0;1],RAANRotationAngle,'Degrees')*...
                Rotation([1;0;0],InclinationRotationAngle,'Degrees')*...
                [0;0;1];
rotate(s, PoleDirection, 0);

FN_i = s.VertexNormals;
%%
load('SE_L4_Vertical.mat');
inc_list = zeros(1,length(T_L4_VL));
for ii = 1:length(T_L4_VL)
    IC = IC_L4_VL(:,ii);
    T = T_L4_VL(ii);
    [t,S] = ode113(@(t,S)CR3BP_n(t,S,u),[0:dt:T],IC,options);
    S = S';

    S_i = zeros(size(S));
    S_i = C2I_primary(S(:,ii),u,DU,VU,t(ii)+5.1+startphase);
    COE_list = State2Coe(S_i,GM_central);
    inc_list(ii) = COE_list(3);
end

%% Simulation paramters %%
CameraAngleCapability=60;
inc_desired = 14.5;
optval = min(abs(inc_list-inc_desired));
[ind_opt] = find(abs(inc_list-inc_desired)==optval);

%%
IC_L4 = IC_L4_VL(:,ind_opt);
T_L4 = 2*pi;
IC_L5 = [IC_L4(1);-IC_L4(2);0;...
         -IC_L4(4);IC_L4(5);IC_L4(6)];

OpenCRTBP_u(u); hold on
L4= DetermineOptimalL4andL5State(IC_L4,T_L4,u,DU,VU,TU,dt);
L5= DetermineOptimalL4andL5State(IC_L5,T_L4,u,DU,VU,TU,dt);
load('SEL1_Lyapunov.mat');

size = 1;

[t,S] = ode113(@(t,S)CR3BP_n(t,S,u),[0:dt:2*pi],IC(:,size),options);
S=S';
S_i = zeros(6,length(t));
for ii = 1:length(t)
    S_i(:,ii) = C2I_primary(S(:,ii),u,DU,VU,t(ii));
    epoch(ii) = datetime(2023,1,1,0,0,0) + seconds(t(ii)*TU);
end
L1.S_i = S_i;
L1.epoch = epoch;

%%
% close all
for ii = 1:12
epoch = ii; % <Jan : 1, Dec : 12>

[~,coveragePercentage(ii)]=PlotSynergy_L145_limb_Apex(L1,L4,L5,epoch,FN_i,CameraAngleCapability,DU,VU,TU,10000);

close all
end
%%

function [ImageBinary,coveragePercentage]=PlotSynergy_L145_limb_Apex(L1,L4,L5,epoch,FN_i,CameraAngleCapability,DU,VU,TU,h_apex)

options=odeset('RelTol',1e-13,'AbsTol',1e-13);
R_sun = 696340;
theta = asind(R_sun/DU);
alpha = acosd(R_sun/(R_sun+h_apex));
beta = acosd(R_sun/(R_sun+h_apex));
Theta_min = 90-alpha-theta;
Theta_max = 90+beta-theta;

temp_time_month = month(L4.epoch);
ind = find(temp_time_month==epoch);
[row,col,~] = size(FN_i);
visibility_disk=zeros(row,col);
visibility_limb=zeros(row,col);


% S_i = L4.S_i;
% parfor ii = 1:row
%     for jj = 1:col
%         normvec = [FN_i(ii,jj,1);FN_i(ii,jj,2);FN_i(ii,jj,3)];
%         for k = ind(1)
%             posvec = S_i(1:3,k);
%             angle_temp = acosd(dot(normvec,posvec)/(norm(normvec)*norm(posvec)));
%             if angle_temp < CameraAngleCapability
%                 visibility_disk(ii,jj) = 1;
%             end
%             if and((Theta_min<angle_temp),(angle_temp<Theta_max))
%                 visibility_limb(ii,jj) = 2;
%             end
%         end
%     end
% end
S_i = L5.S_i;
parfor ii = 1:row
    for jj = 1:col
        normvec = [FN_i(ii,jj,1);FN_i(ii,jj,2);FN_i(ii,jj,3)];
        for k = ind(1)
            posvec = S_i(1:3,k);
            angle_temp = acosd(dot(normvec,posvec)/(norm(normvec)*norm(posvec)));
            if angle_temp < CameraAngleCapability
                visibility_disk(ii,jj) = 1;
            end
            if and((Theta_min<angle_temp),(angle_temp<Theta_max))
                visibility_limb(ii,jj) = 2;
            end
        end
    end
end
S_i = L1.S_i;
parfor ii = 1:row
    for jj = 1:col
        normvec = [FN_i(ii,jj,1);FN_i(ii,jj,2);FN_i(ii,jj,3)];
        for k = ind(1)
            posvec = S_i(1:3,k);
            angle_temp = acosd(dot(normvec,posvec)/(norm(normvec)*norm(posvec)));
            if angle_temp < CameraAngleCapability
                visibility_disk(ii,jj) = 1;
            end
            if and((Theta_min<angle_temp),(angle_temp<Theta_max))
                visibility_limb(ii,jj) = 2;
            end
        end
    end
end

visibility=visibility_disk+visibility_limb;


ImageBinary=mat2gray(visibility);
figure;
hold on;
mesh(ImageBinary,'EdgeColor','interp','FaceColor','interp');
xlabel('Longitude')
ylabel('Latitude')
titlestring = sprintf('L4 Month = %d',epoch);
% title(titlestring)
set(gca,'fontsize',15)
xticks(linspace(0,row,5));
xticklabels({'180W','90W','0','90E','180E'});
yticks(linspace(0,col,5))
yticklabels({'90S','45S','0','45N','90N'});
xlim([0,row]);
ylim([0,col])
colormap("turbo");

counter = 0;
for ii = 250-111:250+111
    for jj = 1:col
        if visibility(ii,jj) == 3
            counter=counter+1;
        end
    end
end



coveragePercentage = counter/(row*col*(80/180));
fprintf('Percent Coverage : %f percent \n\n',coveragePercentage*100)

end